TY - JOUR AU - Borja, E. F. AU - Garay, I. AU - Vidotto, F. PY - 2012 DA - 2012// TI - Learning about Quantum Gravity with a Couple of Nodes T2 - Symmetry Integr. Geom. JO - Symmetry Integrability and Geometry-Methods and Applications SP - 015 EP - 44pp VL - 8 PB - Natl Acad Sci Ukraine, Inst Math KW - discrete gravity KW - canonical quantization KW - spinors KW - spinfoam KW - quantum cosmology AB - Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a simple graph, formed by only two nodes. We review the U(N) framework, which provides a powerful tool for the canonical study of this model, and a formulation of the system based on spinors. We consider also the covariant theory, which permits to derive the model from a more complex formulation, paying special attention to the cosmological interpretation of the theory. SN - 1815-0659 UR - http://arxiv.org/abs/1110.3020 UR - https://doi.org/10.3842/SIGMA.2012.015 DO - 10.3842/SIGMA.2012.015 LA - English N1 - WOS:000303831400001 ID - Borja_etal2012 ER -